# A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing

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## Abstract

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## 1. Introduction

## 2. EEMD, Multi-Scale Fuzzy Entropy, and SVM

#### 2.1. EEMD

- Step 1: Initialize the EMD method. The total operation number is $M$, the amplitude coefficient of added white noise is $k$, and the execution number is $m=1$.
- Step 2: The numerically generated white noise ${x}_{m}(t)$ with the given amplitude to the original signal $x(t)$ is generated:$${x}_{m}(t)=x(t)+k*{N}_{m}(t)$$
- Step 3: The EMD method is used to decompose ${x}_{m}(t)$ into a series of IMF components ${C}_{j,m}$. ${C}_{j,m}$ is the j-th IMF of the m-th decomposition:$${x}_{m}(t)={\displaystyle \sum _{j=1}^{S}{C}_{j,m}}(t)+{r}_{j,m}(t)$$
- Step 4: If the decomposition number is $m<M$, then $m=m+1$. Then, return to Step 2.
- Step 5: The average of the corresponding is calculated for the M-th decomposition. The calculation result is obtained:$${\overline{C}}_{j}(t)=\frac{1}{M}{\displaystyle \sum _{i=1}^{M}{C}_{j,m}}(t)$$

#### 2.2. Fuzzy Entropy

#### 2.3. Multi-Scale Entropy

#### 2.4. Multi-Scale Fuzzy Entropy

#### 2.5. SVM

## 3. Fault Diagnosis Method

## 4. Fault Feature Extraction of the Bearing Fault of AC Motor

#### 4.1. Experimental Environment and Data

#### 4.2. Vibration Signal Decomposition Based on the EEMD Method

#### 4.3. Selection of Major Modes

#### 4.4. Feature Extraction Based on Multi-Scale Fuzzy Entropy

## 5. The Experiment Validation and Result Analysis

#### 5.1. Effectiveness Validation and Comparative Analysis of the Proposed Method

#### 5.2. Diagnosis Results and Analysis under Different Loads

#### 5.3. Diagnosis Results and Analysis under Different Fault Severities

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Yang, Z.X.; Zhong, J.H. A hybrid EEMD-based sampEn and SVD for acoustic signal processing and fault diagnosis. Entropy
**2016**, 18, 112. [Google Scholar] [CrossRef] - Gu, B.; Sheng, V.S.; Wang, Z.J.; Ho, D.; Osman, S.; Li, S. Incremental learning for ν-Support Vector Regression. Neural Netw.
**2015**, 67, 140–150. [Google Scholar] [CrossRef] [PubMed] - Xia, Z.H.; Wang, X.H.; Sun, X.M.; Wang, B.W. Steganalysis of least significant bit matching using multi-order differences. Secur. Commun. Netw.
**2014**, 7, 1283–1291. [Google Scholar] [CrossRef] - Rubini, R.; Meneghetti, U. Application of the envelope and wavelet transform analyses for the diagnosis of incipient faults in ball bearings. Mech. Syst. Signal Process.
**2001**, 15, 287–302. [Google Scholar] [CrossRef] - Zheng, Y.H.; Jeon, B.; Xu, D.H.; Wu, Q.M.J.; Zhang, H. Image segmentation by generalized hierarchical fuzzy C-means algorithm. J. Intell. Fuzzy Syst.
**2015**, 28, 961–973. [Google Scholar] - Seker, S.; Ayaz, E. Feature extraction related to bearing damage in electric motors by wavelet analysis. J. Frankl. Inst.
**2003**, 340, 125–134. [Google Scholar] [CrossRef] - Yang, Y.; Yu, D.J.; Cheng, J.S. A roller bearing fault diagnosis method based on EMD energy entropy and ANN. J. Sound Vib.
**2006**, 294, 269–277. [Google Scholar] - Cheng, J.S.; Yu, D.J.; Yang, Y. A fault diagnosis approach for roller bearings based on EMD method and AR model. Mech. Syst. Signal Process.
**2006**, 20, 350–362. [Google Scholar] - Cheng, J.S.; Yu, D.J.; Tang, J.S.; Yang, Y. Local rub-impact fault diagnosis of the rotor systems based on EMD. Mech. Mach. Theory
**2009**, 44, 784–791. [Google Scholar] [CrossRef] - Immovilli, F.; Bellini, A.; Rubini, R.; Tassoni, C. Diagnosis of bearing faults in induction machines by vibration or current signals: A critical comparison. IEEE Trans. Ind. Appl.
**2010**, 46, 1350–1359. [Google Scholar] [CrossRef] - Lei, Y.G.; He, Z.J.; Zi, Y.Y. EEMD method and WNN for fault diagnosis of locomotive roller bearings. Expert Syst. Appl.
**2011**, 38, 7334–7341. [Google Scholar] [CrossRef] - Wang, D.; Guo, W.; Wang, X.J. A joint sparse wavelet coefficient extraction and adaptive noise reduction method in recovery of weak bearing fault features from a multi-component signal mixture. Appl. Soft Comput. J.
**2013**, 13, 4097–4104. [Google Scholar] [CrossRef] - Liu, T.; Chen, J.; Dong, G.M.; Xiao, W.B.; Zhou, X.N. The fault detection and diagnosis in rolling element bearings using frequency band entropy. J. Mech. Eng. Sci.
**2013**, 227, 87–99. [Google Scholar] [CrossRef] - Wang, Z.P.; Lu, C.; Wang, Z.L.; Liu, H.M.; Fan, H.Z. Fault diagnosis and health assessment for bearings using the Mahalanobis-Taguchi system based on EMD-SVD. Trans. Inst. Meas. Control
**2013**, 35, 798–807. [Google Scholar] [CrossRef] - Liao, Q.; Li, X.B.; Huang, B. Hybrid fault-feature extraction of rolling element bearing via customized-lifting multi-wavelet packet transform. J. Mech. Eng. Sci.
**2014**, 228, 2204–2216. [Google Scholar] [CrossRef] - Wang, H.C.; Chen, J.; Dong, G.M. Feature extraction of rolling bearing’s early weak fault based on EEMD and tunable Q-factor wavelet transform. Mech. Syst. Signal Process.
**2014**, 48, 103–119. [Google Scholar] [CrossRef] - Ahn, J.H.; Kwak, D.H.; Koh, B.H. Fault detection of a roller-bearing system through the EMD of a wavelet denoised signal. Sensors
**2014**, 14, 15022–15038. [Google Scholar] [CrossRef] [PubMed] - Jiang, F.; Zhu, Z.C.; Li, W.; Chen, G.A.; Zhou, G.B. Robust condition monitoring and fault diagnosis of rolling element bearings using improved EEMD and statistical features. Meas. Sci. Technol.
**2014**, 25, 025003. [Google Scholar] [CrossRef] - Zhu, K.H.; Song, X.G.; Xue, D.X. A roller bearing fault diagnosis method based on hierarchical entropy and support vector machine with particle swarm optimization algorithm. Measurement
**2014**, 47, 669–675. [Google Scholar] [CrossRef] - Gao, H.Z.; Liang, L.; Chen, X.G.; Xu, G.H. Feature extraction and recognition for rolling element bearing fault utilizing short-time fourier transform and non-negative matrix factorization. Chin. J. Mech. Eng.
**2015**, 28, 96–105. [Google Scholar] [CrossRef] - Henao, H.; Capolino, G.A.; Manes, F.C.; Filippetti, F.; Bruzzese, C.; Strangas, E.; Pusca, R.; Estima, J.; Martin, R.G.; Shahin, H.K. Trends in fault diagnosis for electrical machines: A review of diagnostic techniques. IEEE Ind. Electron. Mag.
**2014**, 8, 31–42. [Google Scholar] [CrossRef] - Lucia, F.; Ciprian, H.; Lorand, S. Induction machine bearing fault detection by means of statistical processing of the stray flux measurement. IEEE Trans. Ind. Electron.
**2015**, 62, 1846–1854. [Google Scholar] - Wang, D.; Sun, S.L.; Tse, P.W. A general sequential Monte Carlo method based optimal wavelet filter: A Bayesian approach for extracting bearing fault features. Mech. Syst. Signal Process.
**2015**, 52–53, 293–308. [Google Scholar] [CrossRef] - He, W.P.; Zi, Y.Y.; Chen, B.Q.; Wu, F.; He, Z.J. Automatic fault feature extraction of mechanical anomaly on induction motor bearing using ensemble super-wavelet transform. Mech. Syst. Signal Process.
**2015**, 54, 457–480. [Google Scholar] [CrossRef] - Wang, H.C.; Chen, J.; Dong, G.M. Fault diagnosis of rolling bearing’s early weak fault based on minimum entropy de-convolution and fast Kurtogram algorithm. J. Mech. Eng. Sci.
**2015**, 229, 2890–2907. [Google Scholar] [CrossRef] - Wang, C.; Gan, M.; Zhu, C.A. Non-negative EMD manifold for feature extraction in machinery fault diagnosis. Measurement
**2015**, 70, 188–202. [Google Scholar] [CrossRef] - Shi, P.M.; An, S.J.; Li, P.; Han, D.Y. Signal feature extraction based on cascaded multi-stable stochastic resonance denoising and EMD method. Measurement
**2016**, 90, 318–328. [Google Scholar] [CrossRef] - Wang, Y.; Liu, D.; Xu, G.H.; Jian, K.S. An image dimensionality reduction method for rolling bearing fault diagnosis based on singular value decomposition. J. Mech. Eng. Sci.
**2016**, 230, 1830–1845. [Google Scholar] [CrossRef] - Li, Y.B.; Xu, M.Q.; Wei, Y.; Huang, W.H. A new rolling bearing fault diagnosis method based on multiscale permutation entropy and improved support vector machine based binary tree. Measurement
**2016**, 77, 80–94. [Google Scholar] [CrossRef] - Pincus, S.M. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA
**1991**, 88, 2297–2301. [Google Scholar] [CrossRef] [PubMed] - Zhao, S.F.; Liang, L.; Xu, G.H.; Wang, J.; Zhang, W.M. Quantitative diagnosis of a spall-like fault of a rolling element bearing by empirical mode decomposition and the approximate entropy method. Mech. Syst. Signal Process.
**2013**, 40, 154–177. [Google Scholar] [CrossRef] - Richman, J.S.; Moorman, J.R. Physiological time series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol.
**2000**, 278, 2039–2049. [Google Scholar] - Chen, W.; Wang, Z.; Xie, H.; Yu, W. Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans. Neural Syst. Rehabil. Eng.
**2007**, 15, 266–272. [Google Scholar] [CrossRef] [PubMed] - Chen, W.T.; Zhuang, J.; Yu, W.X.; Wang, Z. Measuring complexity using FuzzyEn, ApEn and SampEn. Med. Eng. Phys.
**2009**, 31, 61–68. [Google Scholar] [CrossRef] [PubMed] - Dong, S.J.; Tang, B.P.; Chen, R.X. Bearing running state recognition based on non-extensive wavelet feature scale entropy and support vector machine. Measurement
**2013**, 46, 4189–4199. [Google Scholar] [CrossRef] - Zhang, L.; Xiong, G.L.; Liu, H.S.; Zou, H.J.; Guo, W.Z. Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference. Expert Syst. Appl.
**2010**, 37, 6077–6085. [Google Scholar] [CrossRef] - Liu, H.H.; Han, M.H. A fault diagnosis method based on local mean decomposition and multi-scale entropy for roller bearings. Mech. Mach. Theory
**2014**, 75, 67–78. [Google Scholar] [CrossRef] - Vakharia, V.; Gupta, V.K.; Kankar, P.K. A multiscale permutation entropy based approach to select wavelet for fault diagnosis of ball bearings. J. Vib. Control
**2015**, 21, 3123–3131. [Google Scholar] [CrossRef] - Tiwari, R.; Gupta, V.K.; Kankar, P.K. Bearing fault diagnosis based on multi-scale permutation entropy and adaptive neuro fuzzy classifier. J. Vib. Control
**2015**, 21, 461–467. [Google Scholar] [CrossRef] - Chen, X.; Jin, N.D.; Zhao, A.; Gao, Z.K.; Zhai, L.S.; Sun, B. The experimental signals analysis for bubbly oil-in-water flow using multi-scale weighted-permutation entropy. Physica A
**2015**, 417, 230–244. [Google Scholar] [CrossRef] - Zheng, J.D.; Cheng, J.S.; Yang, Y.; Luo, S.R. A rolling bearing fault diagnosis method based on multi-scale fuzzy entropy and variable predictive model-based class discrimination. Mech. Mach. Theory
**2014**, 78, 187–200. [Google Scholar] [CrossRef] - Costa, M.; Goldberger, A.L.; Peng, C.K. Multiscale entropy analysis of complex phtsiologic time series. Phys. Rev. Lett.
**2002**, 89, 068102. [Google Scholar] [CrossRef] [PubMed] - Wen, X.Z.; Shao, L.; Xue, Y.; Fang, W. A rapid learning algorithm for vehicle classification. Inf. Sci.
**2015**, 295, 395–406. [Google Scholar] [CrossRef] - Gu, B.; Sheng, V.S.; Tay, K.Y.; Romano, W.; Li, S. Incremental Support Vector Learning for Ordinal Regression. IEEE Trans. Neural Netw. Learn. Syst.
**2015**, 26, 1403–1416. [Google Scholar] [CrossRef] [PubMed] - Gu, B.; Sun, X.M.; Sheng, V.S. Structural Minimax Probability Machine. IEEE Trans. Neural Netw. Learn. Syst.
**2016**, PP, 1–11. [Google Scholar] [CrossRef] [PubMed] - Chen, Y.D.; Hao, C.Y.; Wu, W.; Wu, E.H. Robust dense reconstruction by range merging based on confidence estimation. Sci. China Inf. Sci.
**2016**, 59, 092103. [Google Scholar] [CrossRef] - Gu, B.; Sheng, V.S.; Li, S. Bi-parameter space partition for cost-sensitive SVM. In Proceedings of the 24th International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, 25–31 July 2015; pp. 3532–3539.
- Kuo, Y.C.; Hsieh, C.T.; Yau, H.T.; Li, Y.C. Research and Development of a Chaotic Signal Synchronization Error Dynamics-Based Ball Bearing Fault Diagnostor. Entropy
**2014**, 16, 5358–5376. [Google Scholar] [CrossRef] - Wu, S.D.; Wu, C.W.; Wu, T.Y.; Wang, C.C. Multi-scale analysis based ball bearing defect diagnostics using mahalanobis distance and support vector machine. Entropy
**2013**, 15, 416–433. [Google Scholar] [CrossRef] - Bearing Data Center. Available online: http://csegroups.case.edu/bearingdatacenter/home (accessed on 27 December 2016).

Major Modes | Optimal Mode | Suboptimal Mode | Three-Optimal Mode | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{\tau}$ | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |

Entropy Values | 1 | 1.05 | 0.79 | 0.62 | 0.41 | 0.45 | 0.83 | 1.17 | 1.00 | 0.90 | 0.88 | 0.69 | 1.05 | 1.42 | 1.51 | 1.43 |

2 | 1.02 | 0.74 | 0.65 | 0.46 | 0.45 | 0.85 | 1.21 | 1.01 | 0.88 | 0.83 | 0.70 | 1.09 | 1.46 | 1.55 | 1.52 | |

⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | |

40 | 1.06 | 0.78 | 0.64 | 0.43 | 0.51 | 0.86 | 1.18 | 0.96 | 0.89 | 0.80 | 1.69 | 1.07 | 1.42 | 1.50 | 1.43 |

Major Modes | Optimal Mode | Suboptimal Mode | Three-Optimal Mode | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{\tau}$ | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |

Entropy Values | 1 | 0.46 | 0.43 | 0.34 | 0.17 | 0.29 | 0.76 | 0.94 | 0.68 | 0.59 | 0.49 | 0.01 | 0.24 | 0.04 | 0.05 | 0.06 |

2 | 0.44 | 0.43 | 0.32 | 0.17 | 0.29 | 0.80 | 1.03 | 0.76 | 0.60 | 0.56 | 0.00 | 0.01 | 0.01 | 0.02 | 0.02 | |

⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | |

40 | 0.43 | 0.43 | 0.30 | 0.17 | 0.28 | 0.74 | 0.81 | 0.90 | 0.71 | 0.56 | 0.54 | 0.00 | 0.01 | 0.01 | 0.02 |

Major Modes | Optimal Mode | Suboptimal Mode | Three-Optimal Mode | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{\tau}$ | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |

Entropy Values | 1 | 1.05 | 0.75 | 0.84 | 0.37 | 0.61 | 0.64 | 0.78 | 1.00 | 1.23 | 1.28 | 0.01 | 0.01 | 0.02 | 0.03 | 0.04 |

2 | 1.00 | 1.75 | 0.79 | 0.35 | 0.60 | 0.63 | 0.75 | 0.99 | 1.21 | 1.29 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | |

⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ | |

40 | 1.05 | 0.79 | 0.81 | 0.41 | 0.62 | 0.65 | 0.81 | 1.06 | 1.29 | 1.47 | 0.02 | 0.04 | 0.07 | 0.09 | 0.11 |

States | Test Samples | Correctness Diagnosis | Correctness Rate (%) |
---|---|---|---|

Inner race fault | 20 | 20 | 100 |

Outer race fault | 20 | 20 | 100 |

Rolling element fault | 20 | 20 | 100 |

States | Test Samples | EDOFSFD Method | EOMSMFD Method | ||
---|---|---|---|---|---|

Correctness Diagnosis | Correctness (%) | Correctness Diagnosis | Correctness (%) | ||

Inner race fault | 20 | 20 | 100 | 20 | 100 |

Outer race fault | 20 | 20 | 100 | 20 | 100 |

Rolling element fault | 20 | 5 | 25 | 20 | 100 |

States | No-Load and 3HP Loads | |||
---|---|---|---|---|

0.007 in. | 0.021 in. | |||

Test Samples | Correctness Rate (%) | Test Samples | Correctness Rate (%) | |

Inner race fault | 40 | 100 | 40 | 100 |

Outer race fault | 40 | 100 | 40 | 100 |

Rolling element fault | 40 | 100 | 40 | 100 |

Results | Inner Race Fault | Outer Race Fault | Rolling Element Fault | |||
---|---|---|---|---|---|---|

0.007 in. | 0.021 in. | 0.007 in. | 0.021 in. | 0.007 in. | 0.021 in. | |

Correctness rate for classification | 100 | 100 | 100 | 100 | 100 | 100 |

Correctness rate for fault severity | 100 | 100 | 100 | 100 | 95 | 100 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, H.; Sun, M.; Deng, W.; Yang, X. A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing. *Entropy* **2017**, *19*, 14.
https://doi.org/10.3390/e19010014

**AMA Style**

Zhao H, Sun M, Deng W, Yang X. A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing. *Entropy*. 2017; 19(1):14.
https://doi.org/10.3390/e19010014

**Chicago/Turabian Style**

Zhao, Huimin, Meng Sun, Wu Deng, and Xinhua Yang. 2017. "A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing" *Entropy* 19, no. 1: 14.
https://doi.org/10.3390/e19010014